I would profit from a discussion of the purposes, merits,
"general intellectual interest," and so forth of reverse mathematics.
More specifically:
A clear, non-technical statement of what reverse mathematics is
would be appreciated. What makes it "foundational" and how does it fit in
with other subjects in foundations? Is it thought (hoped) that reverse
mathematics will become an important sub-area within foundations? Is the
mathematics of reverse mathematics "good mathematics"? Why? How could a
field that seems so decidedly technical (as r.m.) ultimately be of any
g.i.i.? Does r.m. help to shed light on the question: What is
mathematics? What are some of the presuppositions and intuitions behind
r.m.? In particular, what are the intuitions underlying it that reveal
its importance to all but the "tone deaf"? Does r.m. proceed from a
unifying conception, establishing it to be more than a mere bundle of
techniques?
These are a few overlapping questions that come to mind. Since
Steve and Harvey founded this list at least partly--it appears--to provide
a forum for reverse mathematics, it seems appropriate to raise and discuss
these issues.
Charlie Silver